Fuerteventura for us is all about the white sandy beaches with turquoise waters and moon-like sights. When we went there for the first time, we had a big to-do list, but we ended up just staying on the beach, enjoying the sun and the ocean.
We recommend staying for 3-4 nights in Fuerteventura. It's easily accessible by a short and cheap flight from Tenerife. Also be aware when you go - it's an island of a very strong winds, thus it gets chilly in winter.
We suggest staying in the surfer town of El Cotillo. It is cozy, charming, and full of friendly people, plus it's right next to a very nice beach. So just enjoy the sun and chill. El Cotillo has some really nice design shops: Mojo Art Shop, Lomé Store, Makhoul swimwear, Mouja. For brunch go to Triton's Coffee Lab or Cocoté café & shop pastel. For lunch or dinner book La Vaca Azul (sea food), Tsunami (burgers) or Olivo Corso. Next to El Cotillo is another sufer town Lajares - it's also worth visiting and strolling around. Go to La Panateca for a brunch there.
Go for a hike around Calderón Hondo volcano. Visit a Popcorn beach - it really looks like a beach of popcorns. Spend some time in Dunas de Corralejo dunes. Walk aroun in a charming town of Betancuria. If you want to go to the moon :) go to Mirador de Guise y Ayose viewpoint. We also liked Salinas del Carmen salt museum.
Have we missed anything? Let us know!